Find an equation for the parabola

Question

Find an equation for the parabola that satisfies the given conditions:

 

Focus (2,3)

 

Vertex (2,4)

Answer 1

First, plot the points on graph paper. Since a parabola wraps around the focus, one can tell that the parabola will open down; so "p" will be negative. p = the distance between the focus and vertex; so for this problem, p = 1.

For a vertical parabola, the equation is (x-h)² = 4p(y-k). V(h,k)

(x-2)² = -4(y-4)